
\(T\)  and \(W\)  are even and odd functions under parity, respectively, and together form the angle-dependent supertranslation parameter [1]}, [2]}.
The brackets of the other fermionic symmetries vanish, \([Q_\sigma , Q_{\sigma ^{\prime }}]= 0\) , while there is a non-trivial central charge in the bracket \([G_\epsilon , Q_\sigma ]=-\frac{i}{2}\oint d^{2}x\sqrt{\overline{g}}\left(\epsilon -\epsilon _{0}\right)^{T}\sigma \) .
